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Title: Chebyshev-Fibonacci polynomial relations using generating functions
Authors: Frontczak, Robert
Гой, Тарас Петрович
Hoi, Taras
Keywords: Chebyshev polynomials
Fibonacci sequence
Lucas sequence
generating function
recurrence relation
Issue Date: 2021
Citation: Frontczak R., Goy T. Chebyshev-Fibonacci polynomial relations using generating functions. Integers. 2021. Vol. 21. #A100.
Abstract: The main object of the paper is to reveal connections between Chebyshev polynomials of the fi rst and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved by relating the respective (ordinary and exponential) generating functions to each other. As a consequence, we also establish new combinatorial identities for balancing polynomials and Fibonacci (Lucas) numbers.
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